DCA6108 DISCRETE MATHEMATICS & GRAPH THEORY

Description

SESSION	JAN-FEB 2026
PROGRAM	MASTER OF COMPUTER APPLICATIONS (MCA)
SEMESTER	I
COURSE CODE & NAME	DCA6108  DISCRETE MATHEMATICS & GRAPH THEORY

 

 

Assignment Set – 1

 

 

Q.1. Find the inverse of the matrix A=  using the adjoint method. (10 Marks)

 

Ans 1.

 

Matrix Inverse Using Adjoint Method

The concept of the inverse of a matrice is an essential concept in linear algebra, with numerous applications in solving linear equations in systems, computers, cryptography, and analysis of networks. If a matrix is square, of order n, the inverse exists only when the determinant of A is non-zero. A matrix like this is referred to as invertible or non-singular. The approach of the adjoint is an organized

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Q.2. Use Gauss’s Elimination Method to solve: x – 2y = -4, -5y + z = -9, 4x – 3z = -10. (10 Marks)

Ans 2.

Gauss Elimination Method

Gauss Elimination is one of the most popular direct methods for solving systems that are linear in nature. It is named after the German mathematician Carl Friedrich Gauss and transforms a particular system into an upper triangular structure using the simplest row operations. These include swapping between two rows, multiplying a row with a non-zero scalar and subtracting or adding a multiple of one row

 

 

Q.3. Let f:A→B, g:B→C, and h:C→D. If f(x) = x+1, g(y) = y², and h(z) = √z, find the composition h∘g∘f(x). Also, check the bijectiveness of mappings. (10 Marks)

Ans 3.

Function Composition and Bijectiveness

In math, a function creates a relationship between two sets such that each of the domain is exactly one element in the codomain. Composition of functions can be described as an option of mixing multiple functions, so that the output of one function becomes the input of the following. For functions like f:A and B and the g:B function to C and C, the composition made with f is written as g(f(x)) or (g o f)(x), which maps the elements from A directly into C. Composition is associative in that the h

 

 

 

Assignment Set – 2

 

 

Q.4. Demonstrate that (p ∧ (q ∨ r)) ≡ ((p ∧ q) ∨ (p ∧ r)). (10 Marks)

 

Ans 4.

 

Theory: Distributive Law in Propositional Logic

Propositional logic is a branch of logic which deals with propositions. They’re statements that can be taken as true or false. Logical connectives like conjunction (AND) and disjunction (OR) negation (NOT), implication, and biconditional can be used to make compound propositions out of simple ones. Two complex propositions are considered to be logically similar if they have identical the truth value for every

 

Q.5. The marks scored by students in a test are as follows: [0-20: 6], [20-40: 10], [40-60: 15], [60-80: 8], [80-100: 4]. Find the median marks. (10 Marks)

 

Ans 5.

 

Theory: Median for Grouped Data

The median is a measure of central tendency that represents the middle-point for a set of data points when they are arranged in an order. For grouped frequency distributions, the median does not just represent an observation in the middle, but calculated using a statistical formula that takes into account the classes interval, the cumulative frequencies as well as the class that contains the median. It divides the frequency distribution into two equal portions and fifty percent of the data being be

 

 

Q.6. What is a connected graph? What is a cycle in a graph? (10 Marks)

 

Ans 6.

Connected Graph

The field of Graph Theory is one of discrete maths which studies graphs, which are mathematical models composed of vertices (also known as nodes) as well as edges (also known as arches) which connect two vertices. Graphs are used to model connections and networks within diverse disciplines, such as computer networks social media, transportation systems electrical circuits, as well biological networks. The understanding of the key properties of graphs, such as cycles and connectivity is